Gowdy Spacetimes

In General > s.a. asymptotic flatness at null infinity; models in numerical relativity; solutions of Einstein's equation.
* Idea: Spacetimes with two spacelike Killing vector fields.
* Topology: In the spatially compact case (the Killing vector fields commute) it can be T³ R¹, S³ R¹, or S² S¹ R¹.
* Metric: In the torus case, with partial gauge fixing (and calling x¹ = , one of the angles),

ds² = –N ² dt² + h₁₁ [d + N ¹dt]² + _{a, b = 2, 3} h_ab (dx^a)² .

* Polarized case: Diagonal metrics, only one gravitational degree of freedom; Can be reduced to 2+1 gravity coupled to a massless scalar field.
* Unpolarized case: Less tractable, requires numerical treatment.

References
@ General: Gowdy PRL(71); Misner PRD(73); Gowdy AP(74); Tanimoto JMP(98)gq [generalizations].
@ Exact solutions: Obregón & Ryan gq/98; Ringström MPCPS(04)gq/02; Sánchez et al JMP(04)gq/03 [generating method].
@ Integrals of motion: Manojlovic & Spence NPB(94).
@ Observables: Husain PRD(96)gq [evolution, Ashtekar variables]; Torre CQG(06)gq/05 [polarized, all weak observables].
@ In string theory: Narita et al CQG(00)gq; Cisneros-Pérez et al ht/03-in [and Kantowski-Sachs].
@ With matter: Barbero et al CQG(07)-a0707 [massless scalar fields, canonical].
@ Foliations: Berger et al AP(97); Andréasson CMP(99)gq/98 [Einstein-Vlasov].
@ Asymptotic evolution: Jurke CQG(03)gq/02 [polarized T³]; Berger gq/02/PRD [vacuum].
@ Cauchy horizons: Chrusciel & Lake CQG(04)gq/03; Quevedo GRG(06)gq/04.
@ Related topics: Verdaguer PRP(93) [solitons]; Andersson et al CQG(04)gq/03-in [scale-invariant variables]; Gad ASS(04)gq/04 [energy and momentum distributions]; Gambini et al PRD(05)gq [consistent discretization].

Singularity > s.a. singularities.
* Result: All classical vacuum Gowdy solutions have a singularity.
* Cosmic censorship: Reduce to harmonic map, use behavior of Bel-Robinson tensor.
* Polarized case: Strong cosmic censorship, long time existence and inextendibility, proved; The behavior near the singularity is asymptotically velocity-term dominated.
* Unpolarized case: Same behavior near the singularity found by Berger & Moncrief, but Hern & Stewart disagree.
@ Polarized: Moncrief (81); Moncrief et al; Chrusciel et al CQG(90).
@ Behavior near singularity: Isenberg & Moncrief AP(90) [polarized]; Berger & Moncrief PRD(93), Hern & Stewart CQG(98)gq/97 [unpolarized]; Berger et al gq/97; Berger & Garfinkle PRD(98)gq/97 [on T³, support for AVTD]; Kichenassamy & Rendall CQG(98), Rendall CQG(00)gq [Fuchsian analysis]; Ståhl CQG(02) [S² S¹ and S³, Fuchsian]; Chae & Chrusciel gq/03; Ringström CQG(04).
@ Spikes near singularity: Rendall & Weaver CQG(01)gq; Garfinkle & Weaver PRD(03); Garfinkle CQG(04)gq.

Quantization
@ General references: Berger AP(74); Husain & Smolin NPB(89) [connection representation]; Corichi et al IJMPD(02)gq; Torre PRD(02)gq; Cortez & Mena PRD(05)gq [the unitarity issue]; Torre CQG(07)gq/06 [Schrödinger representation].
@ 3-torus topology: Mena PRD(97)gq [connection representation]; Pierri IJMPD(02)gq/01 [polarized]; Corichi et al PRD(06)gq/05, PRD(06)gq, CQG(06)gq, PRD(07)-a0710 [unitary evolution]; Cortez et al gq/07 [uniqueness of Fock quantization].
@ With matter: Barbero et al CQG(08) [massless scalars, unitary evolution].
@ In supergravity: Macías et al gq/05, PRD(08)-a0801 [N = 1, T³ topology].
@ And singularity, ADM: Berger PLB(82), AP(84); Husain CQG(87).
@ Loop quantization: Banerjee & Date CQG(08)-a0712, CQG(08)- a0712.

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